Royal Astronomical Society. 565 



precession, and refraction, act equally on both stars, or so very 

 nearly so as to leave only an exceedingly small fraction of these cor- 

 rections bearing on the results. And when the stars are very un- 

 equal in magnitude, there is a presumption that the difference of 

 their parallaxes is very nearly equal to the whole parallax of the 

 nearer one. 



The selection of a star for observation involves many considera- 

 tions. In that pitched on by M. Bessel (61 Cygni), the large star 

 so designated, is in fact a fine double star ; nay, one that has been 

 ascertained to be physically double. It is in every respect a highly 

 remarkable star. The mutual distance of its individuals is great, 

 being about 16^". Now this being necessarily less than the axis of 

 their mutual orbit, affords in itself a presumption that the star is a 

 near one. And this presumption is increased by the unusually great 

 proper motion of this binary system, which amounts to nearly 5" 

 per annum, and which has been made by Sir James South the sub- 

 ject of particular inquiry, and found to be not participated in by se- 

 veral small surrounding stars, which, therefore, are not physically 

 connected with it. Moreover, the angular rotation of the two, one 

 about the other, has been well ascertained. 



Now, it fortunately happens, that of these small surrounding 

 stars there are two very advantageously situated for micrometrical 

 comparison with either of the individuals of the binary star, or with 

 the middle point between them. The one of these (a), at a distance 

 of 7' 42", is situated nearly at right angles to the direction of the 

 double star ; the other (b) at a distance of 1 T 46", nearly in that 

 direction. Considering (a) and (b) as fixed points then, and mea- 

 suring at any instant of time their distances from (c), the middle 

 point of the double star, the situation of (c) relative to («) and (b) 

 is ascertained ; and if this be done at every instant, the relative 

 locus of (c), or the curve described by it on the plane of the heaven 

 with respect to the fixed base-line a b, will become known . 



Now, on the hypothesis of parallax, that locus ought to be an 

 ellipse of one certain calculable eccentricity and no other. And its 

 major and minor axes ought to hold with respect to the points, 

 a, b, certain calculable positions and no other. Hence it follows 

 that the distances a c and b c will each of them be subject to annual 

 increase and diminution; and that, 1st, in a given and calculable 

 ratio the one to the other ; and 2dly, so that the maxima and mini- 

 ma of the one distance {a c) shall be nearly contemporaneous with 

 the mean values of the other distance b c, and vice versd. 



Thus we have, in the first place, several particulars independent 

 of mere numerical magnitudes ; and, in the second place, several 

 distinct relations 0, priori determined, to which those numerical 

 values must conform, if it be true that any observed fluctuations in 

 these distances (a b) (a c) be really parallactic. So that if they be 

 found in such conformity, and the above-mentioned maxima and 

 minima do observe that interchangeable law above-stated ; and if, 

 moreover, all due care be proved to have been taken to eliminate 

 every instrumental source of annual fluctuation ; there becomes ac- 



